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[Submitted on 13 Sep 2026] Title:Signed p-adic Residual Encodings of Finite-Domain All-Different Systems with a Sudoku Case Study View a PDF of the paper titled Signed p-adic Residual Encodings of Finite-Domain All-Different Systems with a Sudoku Case Study, by Greg Baker View PDF HTML (experimental) Abstract:We study signed, weighted affine $p$-adic residual objectives as native encodings of finite-domain constraints. For primes that separate the finite alphabet, sufficiently weighted positive unary rows pin each coefficient to its allowed set, while negative rows reward unequal endpoints or clause satisfaction. A coordinatewise domination theorem places every global minimiser in the finite domain; there the loss is, up to an additive constant, the all-different conflict count or the negative number of satisfied CNF clauses. Standard Sudoku provides an $81$-coefficient case study without a one-hot lift. A client-side implementation exposes the generated dataframes, arithmetic, diagnostics, and searches. Comments: 31 pages, 7 figures. Accepted for publication in p-Adic Numbers, Ultrametric Analysis and Applications Subjects: Machine Learning (cs.LG) Cite as: arXiv:2609.16063 [cs.LG] (or arXiv:2609.16063v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.16063 arXiv-issued DOI via DataCite Submission history From: Greg Baker [view email] [v1] Sun, 13 Sep 2026 10:42:59 UTC (528 KB) Full-text links: Access Paper: View a PDF of the paper titled Signed p-adic Residual Encodings of Finite-Domain All-Different Systems with a Sudoku Case Study, by Greg Baker View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)